Prime p₀= 1081995337501807031 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 28 2 64 2 22 2 4 2 52 2 (?)
a_n: 0 2 90 92 120 122 186 188 210 212 216 218 270 272
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 272
Found by: Theadalus
db: batch=76, k=14, 88 28 64 22 4 52

TPT(14)	1081994711522332667	0 2 12 14 24 26 42 44 54 56 174 176 180 182	-625979474364
SPT(16)	1081994816780826877	0 10 24 66 76 90 106 162 244 300 316 330 340 382 396 406	-520720980154
SPT(16)	1081994829937950113	0 20 50 56 80 84 98 138 176 216 230 234 258 264 294 314	-507563856918
SPT(18)	1081994946020741317	0 34 42 64 66 70 76 90 126 130 166 180 186 190 192 214 222 256	-391481065714
SPT(16)	1081994948416910509	0 28 42 72 78 144 148 204 268 324 328 394 400 430 444 472	-389084896522
SPT(16)	1081995237517491287	0 2 44 72 104 170 204 222 254 272 306 372 404 432 474 476	-99984315744
STPT(10)	1081995362958549617	0 2 30 32 42 44 54 56 84 86	25456742586
STPT(10)	1081995503078037617	0 2 24 26 42 44 60 62 84 86	165576230586
SPT(16)	1081995520516689529	0 28 60 70 102 132 190 234 298 342 400 430 462 472 504 532	183014882498
SPT(16)	1081995675326358077	0 6 50 80 84 90 102 126 140 164 176 182 186 216 260 266	337824551046
SPT(16)	1081995728372922563	0 56 68 104 110 114 116 156 158 198 200 204 210 246 258 314	390871115532